I'm currently doing my PhD in Finance. One of my topics is the entropy-based risk estimation methods in stock market. Maybe this research can be interesting for you: https://www.researchgate.net/publication/270221149_Entropy-based_financial_asset_pricing
Another interesting paper, an overview about the application of entropy in finance: http://www.mdpi.com/1099-4300/15/11/4909
I had derived the Shannon Entropy in the Electronic Stock Exchange Network model of General Economic Equilibrium in my PhD thesis at NYU. You can read a further developed version of it in my monograph titled "Bounded Rationality & Incomplete Financial Markets" (I think that is the title) on www.researchgate.net/profile/Soumitra_Mallick.It shows that Genetic Optimisation methods and Arrow of Time principles can interact like forces to give rise to the Shannon Entropy in String condensation (later on developed in Mallick, Hamburger, Mallick (2016, 2017, 2018)). If you wish to you can take a look.